Direct numerical simulation of the turbulent MHD channel flow at low magnetic Reynolds number for electric correlation characteristics

Direct numerical simulation (DNS) of incompressible magnetohydrodynamic (MHD) turbulent channel flow has been performed under the low magnetic Reynolds number assumption.The velocity-electric field and electric-electric field correlations were studied in the present work for different magnetic field orientations.The Kenjeres-Hanjalic (K-H) model was validated with the DNS data in a term by term manner.The numerical results showed that the K-H model makes good predictions for most components of the velocity-electric field correlations.The mechanisms of turbulence suppression were also analyzed for different magnetic field orientations utilizing the DNS data and the K-H model.The results revealed that the dissipative MHD source term is responsible for the turbulence suppression for the case of streamwise and spanwise magnetic orientation,while the Lorentz force which speeds up the near-wall fluid and decreases the production term is responsible for the turbulence suppression for the case of the wall normal magnetic orientation.     

Finite-size particles in turbulent channel flow: quadrant analysis and acceleration statistics

The interaction between finite-size particles and turbulent channel flow in the absence of gravity is studied by direct numerical simulations (DNS). The study is motivated by DNS observations of a turbulent channel flow with high-density, pointwise particles, that cluster in regions of high streamwise root-mean-square (RMS) acceleration close to the wall, contrary to what is observed in homogeneous isotropic turbulence. The aim of the present study is to explore if this is still the case when size effects are taken into account in the DNS. Based on the analysis of the velocity and acceleration statistics, the present DNS shows that, close to the wall, particles with ρ_p/ρ_f ranging from 2 to 4 are surrounded by regions with low streamwise RMS velocity but high streamwise RMS acceleration. According to the normalised particle acceleration probability density functions (PDFs), size effects become important in the near-wall region. As particle inertia increases, the normalised PDFs of particle acceleration tend to a Gaussian distribution. The tails of the normalised PDFs of the fluid conditioned by the presence of particles are higher than that of the unconditioned fluid close to the wall.     

Simulation of viscous flows with undulatory boundaries: Part II. Coupling with other solvers for two-fluid computations

We extend the direct numerical simulation (DNS) capability developed in [D. Yang, L. Shen, Simulation of viscous flows with undulatory boundaries: Part I. Basic solver, J. Comput. Phys. (submitted for publication) ] to the simulation of two-fluid interaction with deformable interface. Two approaches are used to couple the DNS of one fluid with the simulation of another fluid. In the first, the DNS is coupled with a potential-flow based wave solver that uses a high-order spectral (HOS) method. This coupled method is applied to simulate the interaction of turbulent wind with surface waves, including single wave train and broadband wavefield. Validation with previous theoretical and experimental studies shows the accuracy and efficiency of this coupled DNS-HOS method for capturing the essential physics of wind–wave interaction. In the second approach, both of the fluids are simulated by the DNS and are coupled by an efficient iterative scheme, in which the continuity of velocity and the balance of stress are enforced at the interface. The performance of this coupled DNS–DNS method is demonstrated and validated by several test cases including: interfacial wave between two viscous fluids, water surface wave over highly viscous mud flow with interfacial wave, and interaction of two-phase vortex pairs with a deformable interface. Comparison with existing theoretical and numerical results confirms the accuracy of this coupled DNS–DNS method. Finally, this method is applied to study the interaction of air and water turbulence. The nonlinear development of interfacial wave by the excitation of the air and water turbulence, and the wave effect on the instantaneous and statistical characteristics of the turbulence are elucidated.     

Observation of vortex packets in direct numerical simulation of fully turbulent channel flow

A number of experimental studies have inferred the existence of packets of inclined, hairpinlike vortices in wall turbulence on the basis of observations made in two-dimensional x−y planes using visualization and particle image velocimetry (PIV). However, there are very few observations of hairpins in existing three-dimensional studies made using direct numerical simulation (DNS), and no such study claims to have revealed packets. We demonstrate, for the first time, the existence of hairpin vortex packets in DNS of turbulent flow. The vortex packet structure found in the present study at low Reynolds number,Re _t=300, is consistent with and substantiates the observations and the results from twodimensional PIV measurements at higher Reynolds numbers in channel, pipe and boundary layer flows. Thus, the evidence supports the view that vortex packets are a universal feature of wall turbulence, independent of effects due to boundary layer trips or critical conditions in the aforementioned numerical studies. Visualization of the DNS velocity field and vortices also shows the close association of hairpin packets with long low-momentum streaks and the regions of high Reynolds shear stress.     

Vorticity,backscatter and counter-gradient transport predictions using two-level simulation of turbulent flows

The two-level simulation (TLS) method evolves both the large-and the small-scale fields in a two-scale approach and has shown good predictive capabilities in both isotropic and wall-bounded high Reynolds number (Re) turbulent flows in the past. Sensitivity and ability of this modelling approach to predict fundamental features (such as backscatter, counter-gradient turbulent transport, small-scale vorticity, etc.) seen in high Re turbulent flows is assessed here by using two direct numerical simulation (DNS) datasets corresponding to a forced isotropic turbulence at Taylor’s microscale-based Reynolds number Re_λ ≈ 433 and a fully developed turbulent flow in a periodic channel at friction Reynolds number Re_τ ≈ 1000. It is shown that TLS captures the dynamics of local co-/counter-gradient transport and backscatter at the requisite scales of interest. These observations are further confirmed through a posteriori investigation of the flow in a periodic channel at Re_τ = 2000. The results reveal that the TLS method can capture both the large- and the small-scale flow physics in a consistent manner, and at a reduced overall cost when compared to the estimated DNS or wall-resolved LES cost.     

Generalised scale-by-scale energy-budget equations and large-eddy simulations of anisotropic scalar turbulence at various Schmidt numbers

A necessary condition for the accurate prediction of turbulent flows using large-eddy simulation (LES) is the correct representation of energy transfer between the different scales of turbulence in the LES. For scalar turbulence, transfer of energy between turbulent length scales is described by a transport equation for the second moment of the scalar increment. For homogeneous isotropic turbulence, the underlying equation is the well-known Yaglom equation. In the present work, we study the turbulent mixing of a passive scalar with an imposed mean gradient by homogeneous isotropic turbulence. Both direct numerical simulations (DNS) and LES are performed for this configuration at various Schmidt numbers, ranging from 0.11 to 5.56. As the assumptions made in the derivation of the Yaglom equation are violated for the case considered here, a generalised Yaglom equation accounting for anisotropic effects, induced by the mean gradient, is derived in this work. This equation can be interpreted as a scale-by-scale energy-budget equation, as it relates at a certain scale r terms representing the production, turbulent transport, diffusive transport and dissipation of scalar energy. The equation is evaluated for the conducted DNS, followed by a discussion of physical effects present at different scales for various Schmidt numbers. For an analysis of the energy transfer in LES, a generalised Yaglom equation for the second moment of the filtered scalar increment is derived. In this equation, new terms appear due to the interaction between resolved and unresolved scales. In an a-priori test, this filtered energy-budget equation is evaluated by means of explicitly filtered DNS data. In addition, LES calculations of the same configuration are performed, and the energy budget as well as the different terms are thereby analysed in an a-posteriori test. It is shown that LES using an eddy viscosity model is able to fulfil the generalised filtered Yaglom equation for the present configuration. Further, the dependence of the terms appearing in the filtered energy-budget equation on varying Schmidt numbers is discussed.     

A Lagrangian stochastic model for tetrad dispersion

We present results for tetrad (four-particle) dispersion in homogeneous isotropic turbulence by means of a simple Lagrangian stochastic model with a focus on the inertial subrange. We show that for appropriate values of C ₀, the constant of proportionality in the second-order Lagrangian velocity structure function, the shape statistics agree well with equivalent results from a direct numerical simulation (DNS) of turbulence. Moreover, we show that the shape statistics are independent of C ₀ for a wide range of C ₀-values. We also show that the parameters which characterise the shape of the tetrads can be approximately related to appropriate ratios of the growth rates of the mean square separation, the mean square area and the mean square volume of the tetrads. By means of exit times, we are able to estimate the equivalent values for the DNS data. We also consider the statistics of four-point velocity differences (via a diffusion tensor) which agree well with the DNS. We show that the nature of the velocity field experienced by the tetrad varies significantly with C ₀.     

A one-equation turbulence model for recirculating flows

A one-equation turbulence model which relies on the turbulent kinetic energy transport equation has been developed to predict the flow properties of the recirculating flows. The turbulent eddy-viscosity coefficient is computed from a recalibrated Bradshaw’s assumption that the constant a₁ = 0.31 is recalibrated to a function based on a set of direct numerical simulation (DNS) data. The values of dissipation of turbulent kinetic energy consist of the near-wall part and isotropic part, and the isotropic part involves the von Karman length scale as the turbulent length scale. The performance of the new model is evaluated by the results from DNS for fully developed turbulence channel flow with a wide range of Reynolds numbers. However, the computed result of the recirculating flow at the separated bubble of NACA4412 demonstrates that an increase is needed on the turbulent dissipation, and this leads to an advanced tuning on the self-adjusted function. The improved model predicts better results in both the non-equilibrium and equilibrium flows, e.g. channel flows, backward-facing step flow and hump in a channel.     

On generating initial conditions for turbulence models: the case of Rayleigh–Taylor instability turbulent mixing

A new approach to generate initial conditions for RANS simulations of Rayleigh–Taylor (RT) turbulence is presented. The strategy is to provide profiles of turbulent model variables when it is suitable for the turbulence model to be started, and then use these profiles for the turbulence model initialization. The generation of turbulence model variable profiles is achieved with a two-step process. In the first step, a nonlinear modal model assuming small amplitude initial perturbations, incompressible and inviscid fluids is used to track the growth of modes that exist in a given initial perturbation spectrum, and also modes generated by mode interactions. The amplitude development of each mode represents the penetration distance of the light fluid into the heavy fluid (bubble penetration), for a given mode perturbation. The penetration distance of heavy fluid into the light fluid (spike penetration), for a given mode perturbation, is inferred from the bubble's height by an empirical relation valid for small initial amplitudes, and established by DNS simulations that depend on a nondimensional time, and the density contrast (Atwood number). It is hypothesized that the bubble front position of the RT mixing layer can be approximated by the largest penetration distance among all existing modes. The spike front position is approximated in the same fashion. The nonlinear model is evaluated by comparing the bubble front height evolution predicted by the model against the bubble front height predicted by an incompressible implicit large eddy simulations (ILES) code. Comparisons of results for “top-hat” and two-band initial perturbation spectra at Atwood numbers, A_T =0.3 and A_T =0.5 for the former, and A_T =0.01 and A_T =0.5 for the latter, show reasonable agreement. In the second step, the bubble and spike front positions, their derived velocities, and simplified profiles of the mixture fraction distribution of each fluid between the bubble and spike fronts are used with a two-fluid approximation to derive profiles for the turbulence model variables. When initialized with modal model profiles at start time τ₀, (i.e., the time when the turbulence model variable profiles are inferred from the modal model results), the RANS simulations provide at all times τ>τ₀ profiles that show good agreement with ILES simulations. The procedure for determining the time at which the RANS model should be started is a representative use, other parameters can be used depending on the application. In this paper, for the purpose of demonstration of the full strategy, τ₀ is taken as the time at which the mixing layer growth rate parameter α has reached its asymptotic value in the corresponding ILES simulation.     

新型大涡数值模拟亚格子模型及应用

基于湍流大小尺度间动量输运的结构函数方程，提出了一种新的湍流大涡模型(LES)亚格子涡粘模式．新亚格子涡粘系数正比于纵向速度增量的扭率，它表征大小尺度湍流间的能量输运和耗散之比．新模式通过各向同性湍流直接数值模拟数据库的检验，并用于槽道湍流的大涡模拟计算，将所得结果与DNS结果进行了比较．     

Influence of polymer additives on turbulent energy cascading in forced homogeneous isotropic turbulence studied by direct numerical simulations

Direct numerical simulations(DNS) were performed for the forced homogeneous isotropic turbulence(FHIT) with/without polymer additives in order to elaborate the characteristics of the turbulent energy cascading influenced by drag-reducing effects.The finite elastic non-linear extensibility-Peterlin model(FENE-P) was used as the conformation tensor equation for the viscoelastic polymer solution.Detailed analyses of DNS data were carried out in this paper for the turbulence scaling law and the topological dynamics of FHIT as well as the important turbulent parameters,including turbulent kinetic energy spectra,enstrophy and strain,velocity structure function,small-scale intermittency,etc.A natural and straightforward definition for the drag reduction rate was also proposed for the drag-reducing FHIT based on the decrease degree of the turbulent kinetic energy.It was found that the turbulent energy cascading in the FHIT was greatly modified by the drag-reducing polymer additives.The enstrophy and the strain fields in the FHIT of the polymer solution were remarkably weakened as compared with their Newtonian counterparts.The small-scale vortices and the small-scale intermittency were all inhibited by the viscoelastic effects in the FHIT of the polymer solution.However,the scaling law in a fashion of extended self-similarity for the FHIT of the polymer solution,within the presently simulated range of Weissenberg numbers,had no distinct differences compared with that of the Newtonian fluid case.     

Local multifractal thermodynamics of 3D turbulence

Using results of a direct numerical simulation (DNS) of 3D turbulence we show that the observed generalized scaling (i.e. scaling moments versus moments of different orders) is consistent with a lognormal-like distribution of turbulent energy dissipation fluctuations with moderate amplitudes for all space scales available in this DNS (beginning from the molecular viscosity scale up to largest ones). Local multifractal thermodynamics has been developed to interpret the data obtained using the generalized scaling, and a new interval of space scales with inverse cascade of generalized energy has been found between dissipative and inertial intervals of scales for sufficiently large values of the Reynolds number. Received 21 July 2000     

A Web services accessible database of turbulent channel flow and its use for testing a new integral wall model for LES

The output from a direct numerical simulation (DNS) of turbulent channel flow at Re_τ ≈ 1000 is used to construct a publicly and Web services accessible, spatio-temporal database for this flow. The simulated channel has a size of 8πh × 2h × 3πh, where h is the channel half-height. Data are stored at 2048 × 512 × 1536 spatial grid points for a total of 4000 time samples every 5 time steps of the DNS. These cover an entire channel flow-through time, i.e. the time it takes to traverse the entire channel length 8πh at the mean velocity of the bulk flow. Users can access the database through an interface that is based on the Web services model and perform numerical experiments on the slightly over 100 terabytes (TB) DNS data on their remote platforms, such as laptops or local desktops. Additional technical details about the pressure calculation, database interpolation, and differentiation tools are provided in several appendices. As a sample application of the channel flow database, we use it to conduct an a-priori test of a recently introduced integral wall model for large eddy simulation of wall-bounded turbulent flow. The results are compared with those of the equilibrium wall model, showing the strengths of the integral wall model as compared to the equilibrium model.     

Turbulent flame visualization using direct numerical simulation

Combustion phenomena are of high scientific and technological interest, in particular for energy generation and transportation systems. Direct Numerical Simulations (DNS) have become an essential and well established research tool to investigate the structure of turbulent flames, since they do not rely on any approximate turbulence models. In this work two complementary DNS codes are employed to investigate different types of fuels and flame configurations. The code is π³ is a 3-dimensional DNS code using a low-Mach number approximation. Chemistry is described through a tabulation, using two coordinates to enter a database constructed for example with 29 species and 141 reactions for methane combustion. It is used here to investigate the growth of a turbulent premixed flame in a methane-air mixture (Case 1). The second code,Sider is an explicit three-dimensional DNS code solving the fully compressible reactive Navier-Stokes equations, where the chemical processes are computed using a complete reaction scheme, taking into account accurate diffusion properties. It is used here to compute a hydrogen/air turbulent diffusion flame (Case 2), considering 9 chemical species and 38 chemical reactions.     

Diffraction of sound pulses on an elastic spherical shell submerged in an oceanic waveguide

The paper is devoted to simulating an acoustic field scattered by an elastic spherical shell placed in a waveguide with a fluid attenuating bottom. The emitted signal is a wideband pulse with a Gaussian envelope. The normal wave method is used in the frequency domain for calculating the field of a point source in a free waveguide and the shell scattering coefficients. Movement of the receiver along a vertical straight line located behind the shell makes it possible to obtain a “three-dimensional” image of the field scattered by the shell. In this representation, the horizontal axis is time; the vertical axis is the submersion depth of the receiver; the intensity shows the amplitude of the received signal. Such three-dimensional structures make it possible to analyze the dependence of the complex diffraction structure of the acoustic field on receiver depth. In the considered numerical example, a thin, elastic, spherical shell is located near the attenuating fluid bottom.     

Use of Lagrangian statistics for the analysis of the scale separation hypothesis in turbulent channel flow

Turbulence models often involve Reynolds averaging, with a closure providing the Reynolds stress tensor as function of mean velocity gradients, through a turbulence constitutive equation. The main limitation of this linear closure is that it rests on an analogy with kinetic theory. For this analogy to be valid there has to be a scale separation between the mean velocity variations and the turbulent Lagrangian free path whose mean value is the turbulent mixing length. The aim of this work is to better understand this hypothesis from a microscopic point of view. Therefore, fluid elements are tracked in a turbulent channel flow. The flow is resolved by direct numerical simulation (DNS). Statistics on particle trajectories ending on a certain distance y₀ from the wall are computed, leading to estimations of the turbulent mixing length scale and the Knudsen number. Comparing the computed values to the Knudsen number in the case of scale separation, we may know in which region of the flow and to what extent the turbulence constitutive equation is not verified. Finally, a new non-local formulation for predicting the Reynolds stress is proposed.     

确定分布的展向Lorentz力调制下的槽道湍流涡结构

采用直接数值模拟方法,对槽道湍流中确定分布的Lorentz力的流动控制与减阻问题进行研究.讨论了Lorentz力作用于槽道湍流后,流场的特性和涡结构的特性,并对此类Lorentz力对槽道湍流的控制与减阻机理进行了讨论.研究发现:1)Lorentz力诱导的层流流场壁面附近存在梯度极大的展向速度剪切层,该剪切层容易形成流向涡结构;2)在给定合适参数的确定分布的Lorentz力作用下,湍流流场仅剩周期分布的准流向涡;3)与未控制流场相比,控制后的流场中,准流向涡的抬升高度大大降低,从而减小猝发强度,使壁面阻力下降.     

A priori evaluation of large eddy simulation subgrid-scale scalar flux models in isotropic passive-scalar and anisotropic buoyancy-driven homogeneous turbulence

Direct numerical simulation (DNS) of passive (non-buoyant) and active (buoyant) scalar homogeneous turbulence is carried out using a standard pseudo-spectral numerical method. The flow settings simulated include stationary forced and decaying passive-scalar turbulence, as well as decaying anisotropic active-scalar turbulence. The Schmidt number is unity in all cases. The results are compared with, and are found to be in very good agreement with, previous similar DNS studies. The well-validated DNS data are divided into 19 sets, and are employed to study different large eddy simulation (LES) subgrid-scale (SGS) models for the SGS scalar flux. The models examined include three eddy-viscosity-type models (Smagorinsky, Vreman and Sigma with a constant SGS Schmidt number), a Dynamic Structure model and two versions of the Gradient (Gradient and Modulated Gradient) model. The models are investigated with respect to their ability to predict the orientation, and the magnitude, of the SGS scalar flux. Eddy-viscosity models are found to predict the magnitude of the SGS scalar flux accurately, but are poor at predicting the orientation of the SGS scalar flux. The Dynamic Structure and Gradient models are better than eddy-viscosity models at predicting both the magnitude and direction. However, neither of them can be realised in an actual LES, without carrying additional transport equations. Based on these observations, four new models are proposed – combining directions from Dynamic Structure and Gradient models, and magnitudes from Smagorinsky and Vreman eddy-viscosity models. These models are expected to be better than eddy-viscosity and Modulated Gradient models, and this is confirmed by preliminary a posteriori tests.     

A new mixed subgrid-scale model for large eddy simulation of turbulent drag-reducing flows of viscoelastic fluids

A mixed subgrid-scale(SGS) model based on coherent structures and temporal approximate deconvolution(MCT) is proposed for turbulent drag-reducing flows of viscoelastic fluids. The main idea of the MCT SGS model is to perform spatial filtering for the momentum equation and temporal filtering for the conformation tensor transport equation of turbulent flow of viscoelastic fluid, respectively. The MCT model is suitable for large eddy simulation(LES) of turbulent dragreducing flows of viscoelastic fluids in engineering applications since the model parameters can be easily obtained. The LES of forced homogeneous isotropic turbulence(FHIT) with polymer additives and turbulent channel flow with surfactant additives based on MCT SGS model shows excellent agreements with direct numerical simulation(DNS) results. Compared with the LES results using the temporal approximate deconvolution model(TADM) for FHIT with polymer additives, this mixed SGS model MCT behaves better, regarding the enhancement of calculating parameters such as the Reynolds number.For scientific and engineering research, turbulent flows at high Reynolds numbers are expected, so the MCT model can be a more suitable model for the LES of turbulent drag-reducing flows of viscoelastic fluid with polymer or surfactant additives.     

On minimum aspect ratio for duct flow facilities and the role of side walls in generating secondary flows

To the surprise of some of our colleagues, we recently recommended aspect ratios of at least 24 (instead of accepted values over last few decades ranging from 5 to 12) to minimise effects of side walls in turbulent duct flow experiments, in order to approximate the two-dimensional channel flow. Here we compile available results from hydraulics and civil engineering literature, where this was already documented in the 1980s. This is of great importance due to the large amount of computational studies (mainly direct numerical simulations, DNSs) for spanwise-periodic turbulent channel flows, and the extreme complexity of constructing a fully developed duct flow facility with aspect ratio of 24 for high Reynolds numbers with adequate probe resolution. Results from this non-traditional literature for the turbulence community are compared to our recent database of DNS of turbulent duct flows with aspect ratios ranging from 1 to 18 at Re_{τ, c} values of 180 and 330, leading to very good agreement between their experimental and our computational results at these low Reynolds numbers. The DNS results also reveal the complexity of a multitude of streamwise vortical structures in addition to the secondary corner flows (which extend up to z ? 5h). These time-dependent and meandering streamwise structures are located at the core of the duct and scale with its half-height. Comparisons of these structures with the vortical motions found in spanwise-periodic channels reveal similitudes in their time-averages and the same rate of decay of their mean kinetic energy ～ T^{? 1}_A, with T_A being the averaging time. However, differences between the two flows are identified and ideas for their future analysis are proposed.